# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(~(s(t_h4s_integers_int,X1)=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))=>![X2]:s(t_h4s_integers_int,h4s_integers_intu_u_rem(s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,X1))),s(t_h4s_integers_int,X1)))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))),file('i/f/integer/INT__REM__COMMON__FACTOR', ch4s_integers_INTu_u_REMu_u_COMMONu_u_FACTOR)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/integer/INT__REM__COMMON__FACTOR', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/integer/INT__REM__COMMON__FACTOR', aHLu_FALSITY)).
fof(4, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/integer/INT__REM__COMMON__FACTOR', aHLu_BOOLu_CASES)).
fof(23, axiom,![X3]:(s(t_bool,X3)=s(t_bool,f)<=>~(p(s(t_bool,X3)))),file('i/f/integer/INT__REM__COMMON__FACTOR', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(37, axiom,![X8]:s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X8),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))=s(t_h4s_integers_int,X8),file('i/f/integer/INT__REM__COMMON__FACTOR', ah4s_integers_INTu_u_ADDu_u_RID)).
fof(38, axiom,![X1]:p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,h4s_integers_abs(s(t_h4s_integers_int,X1)))))),file('i/f/integer/INT__REM__COMMON__FACTOR', ah4s_integers_INTu_u_ABSu_u_POS)).
fof(39, axiom,![X14]:s(t_h4s_integers_int,h4s_integers_abs(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X14)))))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X14))),file('i/f/integer/INT__REM__COMMON__FACTOR', ah4s_integers_INTu_u_ABSu_u_NUM)).
fof(40, axiom,![X1]:(s(t_h4s_integers_int,h4s_integers_abs(s(t_h4s_integers_int,X1)))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))<=>s(t_h4s_integers_int,X1)=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))),file('i/f/integer/INT__REM__COMMON__FACTOR', ah4s_integers_INTu_u_ABSu_u_EQ0)).
fof(41, axiom,![X13]:![X2]:![X1]:((p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_abs(s(t_h4s_integers_int,X13))),s(t_h4s_integers_int,h4s_integers_abs(s(t_h4s_integers_int,X2))))))&(p(s(t_bool,h4s_bools_cond(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,X1))),s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,X13))),s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X13),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))))))&?[X15]:s(t_h4s_integers_int,X1)=s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,X15),s(t_h4s_integers_int,X2))),s(t_h4s_integers_int,X13)))))=>s(t_h4s_integers_int,h4s_integers_intu_u_rem(s(t_h4s_integers_int,X1),s(t_h4s_integers_int,X2)))=s(t_h4s_integers_int,X13)),file('i/f/integer/INT__REM__COMMON__FACTOR', ah4s_integers_INTu_u_REMu_u_UNIQUE)).
fof(42, axiom,![X9]:![X8]:(p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X8),s(t_h4s_integers_int,X9))))<=>(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X8),s(t_h4s_integers_int,X9))))|s(t_h4s_integers_int,X8)=s(t_h4s_integers_int,X9))),file('i/f/integer/INT__REM__COMMON__FACTOR', ah4s_integers_INTu_u_LEu_u_LT)).
fof(43, axiom,![X7]:![X3]:![X16]:s(X7,h4s_bools_cond(s(t_bool,X16),s(X7,X3),s(X7,X3)))=s(X7,X3),file('i/f/integer/INT__REM__COMMON__FACTOR', ah4s_bools_CONDu_u_ID)).
# SZS output end CNFRefutation
